Volume 9, Issue 3
On the Number of Zeroes of Exponential Systems

J. Comp. Math., 9 (1991), pp. 256-261.

Published online: 1991-09

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• Abstract

A system $E:C^n\rightarrow C^n$ is said to be an exponential one if its terms are $ae^{im_1Z_1}.\cdots .e^{im_nZ_n}$. This paper proves that for almost every exponential system $E:C^n\rightarrow C^n$ with degree $(q_1,\cdots,q_n)$, $E$ has exactly $\Pi^n_j=1(2q_j)$ zeroes in the domain $D=\{(Z_1,\cdots,Z_n)\in C^n:Z_j=x_j+iy_j,x_j,y_j\in R,0\leq x_j<2\pi ,j=1,\cdots,n\}$, and all these zeroes can be located with the homotopy method.

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@Article{JCM-9-256, author = {Gao , Tang-An and Wang , Ze-Ke}, title = {On the Number of Zeroes of Exponential Systems}, journal = {Journal of Computational Mathematics}, year = {1991}, volume = {9}, number = {3}, pages = {256--261}, abstract = {

A system $E:C^n\rightarrow C^n$ is said to be an exponential one if its terms are $ae^{im_1Z_1}.\cdots .e^{im_nZ_n}$. This paper proves that for almost every exponential system $E:C^n\rightarrow C^n$ with degree $(q_1,\cdots,q_n)$, $E$ has exactly $\Pi^n_j=1(2q_j)$ zeroes in the domain $D=\{(Z_1,\cdots,Z_n)\in C^n:Z_j=x_j+iy_j,x_j,y_j\in R,0\leq x_j<2\pi ,j=1,\cdots,n\}$, and all these zeroes can be located with the homotopy method.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9399.html} }
TY - JOUR T1 - On the Number of Zeroes of Exponential Systems AU - Gao , Tang-An AU - Wang , Ze-Ke JO - Journal of Computational Mathematics VL - 3 SP - 256 EP - 261 PY - 1991 DA - 1991/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9399.html KW - AB -

A system $E:C^n\rightarrow C^n$ is said to be an exponential one if its terms are $ae^{im_1Z_1}.\cdots .e^{im_nZ_n}$. This paper proves that for almost every exponential system $E:C^n\rightarrow C^n$ with degree $(q_1,\cdots,q_n)$, $E$ has exactly $\Pi^n_j=1(2q_j)$ zeroes in the domain $D=\{(Z_1,\cdots,Z_n)\in C^n:Z_j=x_j+iy_j,x_j,y_j\in R,0\leq x_j<2\pi ,j=1,\cdots,n\}$, and all these zeroes can be located with the homotopy method.

Tang-An Gao & Ze-Ke Wang. (1970). On the Number of Zeroes of Exponential Systems. Journal of Computational Mathematics. 9 (3). 256-261. doi:
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